Due and Scope
Due: [insert date]. Submit calculations, one relative-age sketch or table, and concise written interpretations.
Learning objectives: infer surface ages from crater counts and cross-cutting relations; compare atmospheric escape; apply albedo and energy balance; distinguish observation from climate interpretation.
Instructions: Use units throughout. State assumptions about equal areas, impact rates, preservation, and greenhouse forcing. Revisions may be resubmitted with a change note.
Problems
1. Crater Counts and Resurfacing 25 points
Two equal-area image tiles on the same planet cover \(1.0\times10^5\,\mathrm{km^2}\) each. Tile A has 84 craters larger than 2 km. Tile B has 12 craters larger than 2 km and a smooth lava plain crossing older crater rims.
- Compute crater density for each tile in craters per \(10^5\,\mathrm{km^2}\).
- Compute the ratio of crater densities.
- Rank the tiles by relative surface age and cite the evidence.
- State two assumptions that could make the age inference unreliable.
Deliverables: crater-density table, ratio, and age interpretation.
2. Cross-Cutting Sequence on a Terrestrial Surface 25 points
An image shows these relationships: a large crater cuts highland terrain; a lava flow fills the crater floor; a wrinkle ridge crosses the lava flow; a small fresh crater sits on top of the ridge with bright rays; wind streaks extend from the fresh crater.
- List the five events from oldest to youngest.
- For each ordering step, state the stratigraphic rule or observation used.
- Explain how illumination angle or image scale could mislead the interpretation.
Deliverables: ordered event list with evidence notes and one imaging caveat paragraph.
3. Escape Speed and Atmospheric Retention 25 points
Use \(v_{esc}=11.2\,\mathrm{km\ s^{-1}}\sqrt{(M/M_E)/(R/R_E)}\). Compare Earth, Mars \((M=0.107M_E, R=0.532R_E)\), and Venus \((M=0.815M_E, R=0.949R_E)\).
- Compute escape speed for Mars and Venus.
- Rank Earth, Mars, and Venus by escape speed.
- Explain why escape speed alone does not determine present atmosphere thickness.
- Name two additional variables that control atmospheric loss or retention.
Deliverables: escape-speed calculations, ranking, and interpretation.
4. Albedo, Solar Flux, and Greenhouse Interpretation 25 points
Use absorbed solar flux \(F_{abs}=S(1-A)/4\). At Earth's orbit \(S=1361\,\mathrm{W\ m^{-2}}\). Planet C orbits at 0.72 AU with albedo 0.75. Planet D orbits at 1.52 AU with albedo 0.25. Assume solar flux scales as \(1/r^2\).
- Compute \(S\) at each planet.
- Compute absorbed flux for each planet.
- Which absorbs more sunlight per square meter?
- Explain why the planet that absorbs more sunlight need not have the higher surface temperature once greenhouse effect and atmospheric pressure are included.
Deliverables: flux calculations with units and a climate-interpretation paragraph.
OpenStax Companion Practice
Recommended for additional practice: OpenStax Astronomy 2e, Chapter 8, Review Questions 14-16 and Figuring for Yourself 34; Chapter 10, Review Questions 2, 4, 6, 8, and 10; Thought Questions 19, 22, 24, and 27; Figuring for Yourself 28 and 30. Verify numbering against the adopted PDF before LMS release.